Rewrite as a simplified fraction. ${1.62\overline{7} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1627.7777...\\ 100x &= 162.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1465}$ ${x = \dfrac{1465}{900}} $ ${x = \dfrac{293}{180}} \text{or} {1 \dfrac{113}{180}}$